Differential viscometer with solvent compressibility correction

ABSTRACT

An improved version of the capillary bridge viscometer that compensates for the effect of solvent compressibility is disclosed. A novel, yet simple and inexpensive modification to a conventional capillary bridge viscometer design can improve its ability to reject pump pulses by more than order of magnitude. This improves the data quality and allows for the use of less expensive pumps. A pulse compensation volume is added such that it transmits pressure to the differential pressure transducer without sample flowing there through. The pressure compensation volume enables the cancellation of the confounding effects of pump pulses in a capillary bridge viscometer.

PRIORITY

This application is a continuation of U.S. patent application Ser. No.15/736,291, filed Dec. 13, 20179.

BACKGROUND

To understand the role that pump pulses play in the measurement ofspecific viscosity it is instructive to first consider the singlecapillary viscometer as shown in FIG. 1 . A pump 101 draws fluid from areservoir 102 and passes it through a sensing capillary 103. Adifferential transducer 104 measures the pressure across the capillary.The measured pressure is proportional to the flow rate and the sampleviscosity. If one first flows solvent through the capillary and measuresthe pressure P₀, and subsequently injects a sample, the specificviscosity is simplyη_(sp) =P _(s) /P ₀  (1)If the sample composition varies over in time, as is the case with theelution of a chromatographic separation, the specific viscosity as afunction of time is simplyη_(sp)(t)=P _(s)(t)/P ₀.

A problem arising from such a flowing system is that if the pump is notperfectly stable, pressure pulses appear identical to changes in thesample viscosity. Since the output of the conventional viscometer isdirectly proportional to the pressure, the sensitivity of such a deviceis limited by the quality of the pump used. High quality chromatographysolvent delivery systems commonly provide solvent with pressure pulsesless than 0.1%, so the ability to measure specific viscosity is limitedto this level. However, high quality viscometers, such as the ViscoStar®(Wyatt Technology Corporation, Santa Barbara, Calif.) are able toroutinely measures specific viscosity down to 1E-6, which is threeorders of magnitude smaller, and therefore the improved sensitivity ofmeasurements from high quality viscometers such as these is lost in thenoise of the pump pulses from chromatography systems employing even thefinest pumps available.

As an example of the output of a single capillary viscometer considerthe chromatographic elution shown in FIG. 2 . Two mg of Bovine SeriumAlbumen (BSA) was injected on a protein column (Wyatt Technology, SantaBarbara, Calif.) at a flow rate of 0.6667 ml/min, and the solvent wasphosphate buffered saline. The pump was an Agilent® 1100 series pump(Agilent Technologies, Santa Clara, Calif.). As the detector ispositioned after the column, the pump pulses are further dampened. Inline following the viscometer was a Optilab® rEX concentration detector(Wyatt Technology Corporation, Santa Barbara, Calif.) that measured thedifferential refractive index 201 of the resulting elution. In spite ofthe fact that a high quality chromatography pump was used, the pumppulses limit the performance as is evident in the viscometry data 202.

One way to ameliorate the problem of pump pulses masquerading as samplepeaks is to use a capillary bridge viscometer such as that described byHaney in 1982 in U.S. Pat. No. 4,463,598. The capillary bridgeviscometer is a fluid analog of the classical Wheatstone bridgeelectrical circuit in which four capillaries are connected in a bridgeformation along with a large fluid reservoir in one of the lower bridgearms. The delay volume insures that the bridge will go out of balancewhen a sample is introduced to the bridge. Data can be taken until thesample emerges from the delay column at which time one must wait for thecolumn to refill with solvent before another sample may be injected. Theout-of balance pressure is measured by a differential pressuretransducer (DP), and the pressure from top to bottom of the bridge ismeasured by a separate transducer (IP). These two signals can becombined to determine the specific viscosity, η_(sp), through therelation

$\begin{matrix}{\eta_{sp} = {{\frac{\eta_{s}}{\eta_{0}} - 1} = \frac{4DP}{{IP} - {2DP}}}} & (2)\end{matrix}$where η_(s) is the sample viscosity, and η₀ is the solvent viscosity. Ifthe pump that drives the fluid through the system is not perfectlystable the system pressure, as well as the flow rate, fluctuateperiodically. The assumption is that both sides of the DP transducerexperience the same pressure pulses so that the differential nature ofthe transducers cancels out the pressure pulses. When the bridge isfilled with pure solvent the DP signal should always equal zero.

By contrast, the IP transducer experiences no such cancellation. This isclear if one considers the Thévenin equivalent circuit associated withthe bridge, as shown in FIG. 3 . The bridge appears to be two seriescapillaries of impedance R (the left side of the bridge) in parallelwith two series capillaries of impedance R (the right side of thebridge). The resulting circuit as seen by the IP transducer is simply asingle capillary of impedance R. Therefore the IP transducer acts, forall intents and purposes, as a single capillary viscometer, with all ofthe problems of pump pulse pickup.

FIG. 4 presents data from a single capillary viscometer taken from achromatographic elution of Bovine Serum Albumin (BSA) fractionated by asize exclusion column. The DP signal 401 is nearly free of pump pulses,whereas the IP signal 402 is not. The primary problem with the strongpump pulse reduction seen in FIG. 4 is that much of the benefit seen isnot due to bridge cancellation. Instead pump pulses are suppressedbecause the DP sensor has a very slow time constant (˜9 seconds) and isacting as a low pass filter, thus not offering the advantage of highresolution one expects from a high quality viscometer.

The time constant of the sensors in the system can be determined byperforming a simple experiment. FIG. 5 shows the response of theinstrument to a rapid change in the applied flow rate from 0.5 ml/min to1.0 ml/min. The IP signal 501 jumps from 5.5 psi to 11 psi as expected,and equilibrates to the new valve with a time constant around 0.5seconds. The DP signal 502, in contrast, has an initial perturbation andequilibrates to a new equilibrium value with a 9 second time constant.

The low pass filtering that occurs from slow sensors works well toeliminate pulses when the pressure oscillations are much faster than thecharacteristic time scale of the underlying peak. In the example shownin FIG. 6 , a standard ViscoStar® H viscometer (Wyatt TechnologyCorporation, Santa Barbara, Calif.) equipped with a Validyne pressuretransducer (Validyne Engineering, Northridge, Calif.) was used tomeasure a sample peak. The peak consisted of 100 μl of 2 mg/ml BSAinjected directly into the viscometer. The flow rate was 0.6667 ml/min.The viscometer was configured with only the short delay column to reducethe sample runs to only a few minutes. The Validyne transducer has atime constant of around 9 seconds, and the pump pulses at this flow ratehave a fundamental period of 1.85 seconds (frequency=0.54 Hz). The peakwidth is 30 seconds. Since the pump pulses are much faster than thesensor time constant it is undeniably effective at suppressing them.

Consider the difference in performance between using a slow sensor and afast one. FIG. 7 shows data taken with the same system configured withDP86 transducers (Measurement Specialties, Fremont, Calif.).Measurements showed that these transducers have a time constant around0.2 seconds in this system. As seen in FIG. 7 , the pump pulses are veryobvious. Therefore it can be deduced that the pulses were alwayspresent, but the Validyne transducers, because of their slow response,were suppressing them.

The problem with suppressing pump pulses by using a slow sensor ora lowpass filter is that the sample peak is also distorted. To make thisclear the data in FIG. 7 subjected to a 9 second moving average filterto simulate the effect of a slow transducer. The results are shown inFIG. 8 . Contrast the raw signal 801 with the filtered data 802. Asexpected, the filtered data is nearly free from pump pulses, but theunderlying peak is distorted. This will negatively impact the accuracyof any results derived from the distorted data. Moreover, recent trendsin the chromatography industry have been working towards the improvementof peak resolution and shorten run times. New generations of uPLCchromatography systems have peaks that are only 10 seconds wide (orless). As peaks become narrower, the measured signals becomeprogressively more distorted. Clearly using slow sensors to suppresspump pulses does not scale well.

A BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 Shows a single capillary viscometer. Sample is injected betweenthe pump and the viscometer and the pressure drop across the capillaryis measured with a differential pressure transducer.

FIG. 2 is a comparison of differential refractive index and singlecapillary viscometer measurements. Pump pulses cause the high frequencyoscillations in the pressure.

FIG. 3 shows a Thévenin equivalent circuit of the capillary bridge. Thefour impedances look to the IP transducer like a single capillary withan impedance of R.

FIG. 4 shows data collected for IP and DP signals from BSA elution.

FIG. 5 shows the results of changing flow rate from 0.5 ml/min to 1.0ml/min. The IP settles to a new value with a 0.5 second time constant,whereas the DP signal, after the initial perturbation, settles to a newvalue with a 9 second time constant.

FIG. 6 is a simulated sample peak measured by a standard viscometerequipped with a short delay column. Pickup of pump pulses is notevident.

FIG. 7 shows data from the same configuration as that used to generatethe data from FIG. 6 , but with DP86 transducers that have a timeconstant of approximately 0.2 seconds. Pump pulses are very obvious.

FIG. 8 shows the effect of a low pass filter at removing pump pulses.Low pass filtering strongly suppresses the pulses but at the expense ofdistorted peaks.

FIG. 9 explains, in graphical terms, the definition of IPA and DPA.

FIG. 10 shows an experiment in which the flow rate was changed abruptlyfrom 0.5 ml/min to 0.6667 ml/min. The IP pressure is on the right axis.The DP pressure is on the left axis. IP changes smoothly between the 5.4psi and 7.2 psi. The DP sensor overshoots its final pressure.

FIG. 11 illustrates the flow rate changes during an overshoot event. Thearrows denote the relative magnitude of the flow in various parts of thebridge.

FIG. 12 an illustration of the absolute pressure on both sides of the DPtransducer during a flow rate step. Both the right and left sides of thebridge increase at different rates. Note this illustration assumes thatthe bridge is perfectly balanced so that DP₊ and DP⁻ reach the samefinal value. For an imperfectly balanced bridge, the overall results arethe same but with a small offset in the final values.

FIG. 13 shows the difference of two signals of the example shown in FIG.12 .

FIG. 14 is the actual overshoot data from the experiment of FIG. 10 fitto the difference of exponential model above. The points are the dataand the overlaying line is the fit.

FIG. 15 shows a novel modification of the 4 capillary bridge design toinclude Pulse Compensation (PC).

FIG. 16 shows the suppression ratio as a function of the PC tubinglength for 0.050″ ID stainless steel tubing.

FIG. 17 shows the suppression ratio as a function of length of the PCfor 0.030″ ID PEEK tubing.

DETAILED DESCRIPTION OF THE INVENTION

A novel modification to conventional viscometric measurement systems cancorrect the time constant mismatch that is inherent to conventionalcapillary bridge designs. An additional volume is added to the systemwhich compensates for the pump pulses which traditionally limit thepossible sensitivity of measurements.

Rather than relying on slow transducers or low pass filtering tosuppress pump pulses, it is much better to understand what limits thebridge's ability to prevent them in the first place. In order toquantify the effectiveness of the pump pulse cancellation the followingmetric will be used. The amplitude suppression ratio is defined as:SR _(a) =IPA/DPA  (3)where IPA is the amplitude of the pump pulses as measured by the IPtransducer, and DPA is the amplitude of pulses measured by DPtransducer.

FIG. 9 shows the IP 901 signal plotted on the right axis and the DPsignal 902 plotted on the left axis. The solvent was PBS flowing at0.6667 ml/min pumped by a Shimadzu LC-20AD solvent delivery module(Shimadzu Corporation, Kyoto, Japan). The pump was stabilized by flowingthe solvent through 10 ft of 0.005″ ID polyether ether ketone (PEEK)tubing before it flowed into the viscometer. This creates about 1000 psiback-pressure on the pump. The combination of back-pressure andexpansion of the PEEK tubing acts as a simple pulse dampener.

Defining the suppression ratio in this way gives a quantitative measureof how effectively the bridge suppresses pump pulses. If the bridge wereworking perfectly, the suppression ratio would be infinite. In theexample shown in FIG. 9 , IPA=6E-3 psi 903 and DPA=8E-4 psi 904, so thesuppression ratio is 7.5, meaning that pump pulses as seen by the DPtransducer are 7.5 smaller than those seen by the IP transducer.

Although the amplitude suppression ratio measures the peak-to-peakexcursions, is worth noting that the suppression is a function offrequency. The frequency dependent suppression ratio is defined asSR(ω)=|IP(ω)/DP(ω)|  (4)where IP(ω) and DP(ω) are the Fourier Transforms of IP(t) and DP(t)respectively. For the rest of the discussion only the suppression ratioSR(ω₀), where a is the fundamental pump frequency will be considered.The advantage to using this definition is that it is less sensitive tothe intrinsic noise of the detectors and the measurement system. Itbetter characterizes the performance of the underlying bridge's abilityto cancel the pump pulses.

For the Shimadzu pump used in these experiments, running at 0.6667ml/min, the fundamental frequency is o=0.54 Hz. For the data in FIG. 9 ,SR(0.54 Hz)=17, which means that the bridge suppresses pump pulses bythis amount at the fundamental frequency of the pump. The reason thatthe suppression ratio at the pump frequency is higher than the amplitudesuppression ratio is that higher frequency harmonics are not suppressedas strongly as the fundamental. For the rest of the discussion all datawas taken at 0.667 ml/min and SR will refer to SR(ω₀).

One key feature of the bridge design is that the delay columns aredesigned to have a large internal volume, but a vanishingly small flowimpedance. This is accomplished by filling columns with large diameterbeads. Because the interstices are large, the flow impedance is verylow. The ViscoStar viscometer (Wyatt Technology Corporation, SantaBarbara, Calif.), for example, uses 0.4 mm diameter ZrSiO2 beads. Theopen space accessible to the sample fluid is 8.1 ml. This can becompared to the individual capillaries, which are 0.25 mm ID and 660 mmlong with an internal volume of 33 μl. The pressure drop across thedelay volume is less than 1% of the pressure drop across the measurementcapillaries. The bridge is balanced with the columns installed so thatthe pressure drop across the DP transducer is adjusted to nearly zerowhen there is pure solvent flowing. The pressure drop across the columnhas a negligible effect on the calculation of the specific viscosity,although as will be argued below the delay volume plays an unexpectedrole in limiting the ability of the bridge to cancel pump pulses.

If the column is ignored in the analysis, the bridge is essentiallysymmetric. Both sides of the DP transducer should see pump pulsesequally. Since DP is a differential sensor, any common mode signal, suchas the pump pulses, will cancel and the suppression ratio shoulddiverge. The actual suppression ratio is around 17. So the question mustbe asked, why are pump pulses not better cancelled?

Of course the presence of the delay column in the left side of thebridge breaks the symmetry. One of the main goals of this disclosure isto understand how this affects the data and how it can be corrected. Onecould imagine several possible mechanisms whereby breaking theleft-right symmetry of the bridge will spoil the pump pulsecancellation. Consider the following observations that help shed lighton this question.

First is that the pump pulses are positively correlated with the signalseen by the P transducer. When the P signal is high, the DP signal isalso high. However if the bridge were truly symmetric, there would benothing to distinguish the DP+ side from the DP− side. One would expectany given realization of the bridge would sometimes be positivelycorrelated and sometimes negatively correlated, but this is not thecase; they are always positively correlated. When the DP transducer isreversed (with the + and − sides ports switched) the effect reverses.This implies that the side that is opposite of the delay column iscorrelated with the IP. When transducers from different vendors areused, the effect is persistent showing that the effect is not somehowbeing generated inside the transducer.

The next observation is that if one puts in a smaller delay column, thesuppression ratio increases. This is not surprising since by making thedelay volume smaller, the system becomes more symmetric. In the limitwhere the delay volume is eliminated, the suppression ratio rises byover an order of magnitude. However, this is of academic interest sincedelay volume is required for the system to be used to measure specificviscosity.

The final observation is to consider what happens when the flow rate ischanged abruptly. FIG. 10 shows the change in the baseline when the flowrate is abruptly changed from 0.5 ml/min to 0.6667 ml/min. The IPtransducer signal 1001 increases smoothly from around 5.4 psi to 7.2psi. The time scale for this change is presumably from a combination ofhow quickly the pump was able to change the flow rate, and the timeconstant of the transducer. More interesting is what happens to the DPsignal 1002. The baseline changes from 0.051 psi to 0.060 psi. If thefour bridge capillaries were perfectly matched, the baseline would bezero for all flow rates. If this system is slightly out of balance, asis the case here, the change in the baseline is proportional to theapplied flow rate. However the salient point is that the signalovershoots the new baseline. Consider the implications that this has forflow in the bridge.

FIG. 11 presents a simple model of the pressure change on either side ofthe DP transducer 1101. As the flow rate is stepped the absolutepressure on both sides of the DP transducer 1101 must increase. We willdenote the pressure on the negative side as DP⁻(t) 1102 and the pressureon the positive side as DP(t) 1103. During the overshoot event we knowthat DP(t)=DP₊(t)−DP⁻(t) is larger than its final equilibrium value.Therefore the pressure on the positive 1103 side of the transducer ishigher than on the negative side 1102. The implication therefore is thatthe pressure difference, and therefore the flow rate, on the upper leftcapillary 1104 is higher than on the upper right capillary 1105. This isdenoted in FIG. 11 by the thickness of the lined arrows. Similarly theflow through the lower left capillary 1106 after the delay volume 1107is lower than through the lower right capillary 1108. Schematically thepressure of the two sides of the bridge are shown in FIG. 12 by thetraces of DP₊(t) 1201 and DP⁻(t) 1202. The difference between the twosignals shown in FIG. 12 has an overshoot that is shown in FIG. 13 .

The data shown in FIG. 10 can be fit a model including an offset torepresent the imperfect bridge balance. The result is shown in FIG. 14 .The time scale of the overshoot 1401 is approximately 3 seconds and theamplitude 1402 is 0.004 psi. The measured pressure data are overlaidwith the fit to the modelDP(t)=a+b exp(−c ₁ t)−d exp(−c ₂ t)  (5)where a, b, c₁, c₂, and dare adjustable parameters.

This model assumes that the flow rate in the upper left capillary ishigher than that in the lower left capillary. Since the two capillariesare in series, this appears to be a contradiction. However the fit tothe model suggests that this is true.

It is not a contradiction if we assume that during the overshoot event,fluid accumulates in the delay volume. There are two possible scenarioswhereby this could happen. The first scenario is if the volume insidedelay column is changing in response to the increased pressure. Thesecond scenario is if the fluid is compressing in response to thechanging pressure. In order to evaluate the relative magnitude of thesetwo hypotheses, we can estimate how much fluid is accumulated by lookingat the size of the overshoot shown in FIG. 14 . The volume of theaccumulated fluid is roughly Δv=QtΔp/p where Q is the volume flow ratethrough the capillary (˜0.25 ml/min), t is time (˜3 sec), Δp is theamplitude of the overshoot (˜0.004 psi) and p is the local pressure(˜2.5 psi). Putting all of this together gives a rough estimate of Δv≈20nL.

The change in volume of the delay columns can be determined by thewell-known formula for the expansion of a pressurized cylinder

$\begin{matrix}{{\Delta v} = {\frac{\Delta pd}{4TE}\left( {5 - {4v}} \right)V}} & (6)\end{matrix}$where Δv is the change in volume, Δp is the change in pressure, d is theinner diameter of the tube, T is the wall thickness, E is Young'sModulus, and v is Poisson's ratio. When evaluated for the tubing in thedelay volume the result is Δv=6 nL which is smaller than the expectedeffect.

Similarly one can evaluate how much the solvent compresses. Water has avery low compressibility of 4.6×10⁻¹⁰ Pa⁻¹. The delay column has aninternal volume of approximately 8.1 mL and the pressure change isaround 0.85 psi (=6 kPa), so that the resulting change in volume isapproximately ΔV˜20 nL, which is consistent with the expected size oftheeffect. The conclusion is that the overshoot is due to a mismatch in thetime constant for pressure changes to equilibrate on the two sides ofthe DP transducer. The source of this time constant mismatch is acombination of solvent compressibility and tubing expansion.

Fortunately this time constant mismatch can be corrected with amodification of the capillary bridge design. Consider the bridge shownin FIG. 15 , which represents an embodiment of the invention within acapillary bridge viscometer system with the novel addition of anadditional pulse compensation volume 1501. This is a large volume offluid that is intended to balance the compressibility of the fluid inthe delay columns.

The pulse compensation (PC) volume 1501 cannot be put in series with themeasurement capillaries or it would affect the viscosity measurement. Byputting it between DP+ 1502 and the T-union 1503 connecting R2 and R4,none of the sample passes through it. It simply transmits the pressureto the sensor. One can adjust the volume in PC until it matches thatfrom the delay columns 1504. When the valves V2 and V3 are actuated (DPPurge), the PC volume 1501 is flushed along with the interior of the DPtransducer. One does not have to put the PC in series with thetransducer; one could equally well put it on a separate T connectionbetween R2 and R4, but in this location it would require an additionalvalve to flush it and eliminate bubbles and trapped fluid. The PC couldtake the form of a delay column like that in the left arm but since thesample never flows through PC a long length of capillary works as well.Indeed using a long length of capillary tubing is less expensive andmore compact.

FIG. 16 shows the effect of varying the length of 0.050″ ID capillarytubing used as the PC volume. As the length of the capillary increases,the suppression ratio grows until it reaches a maximum around 23 ft, atwhich point the volume of the PC is 8.4 mL. The delay columns on thelower left side of the bridge have an aggregate interior volume of 22.5mL, but they are filled with a packed powder of spherical beads. Thespace accessible by the fluid depends on how tightly the beads arepacked, but an optimal random close pack of spheres fills 64%, leaving36% open to the fluid. Therefore the total volume in the delay columnsis approximately 22.5 mL*0.36=8.1 mL. This represents a lower bound. Ifthe beads are not perfectly packed, the actual volume may be slightlyhigher. Therefore the peak suppression ratio occurs when the PC volumematches the open space in the delay volumes. The peak suppression ratiois nearly two orders of magnitude higher than the standard bridge, andthe parasitic noise from pump pulses is essentially eliminated. This isa primary goal of this invention. The improved design increases thesystem sensitivity while simultaneously allowing for the use of lessexpensive pumps.

The data presented in the previous section argue strongly that the pulsecompensation tubing balances the compressibility of the solvent, and toa lesser extent the volume expansion of the delay volume tubing. Anotherway to test this hypothesis is by switching to a solvent that has adifferent compressibility to see if the system is remains balanced. If,as the argument above suggests, the primary effect is due to solventcompressibility and not expansion of the delay volume and capillaries,the system will remain balanced when the solvent is changed. To thatend, the solvent was switched from water to toluene, and the suppressionratio was re-measured. The data was taken at the same flow rate (0.6667ml/min) but a different pump system was used. The fundamental pulsefrequency, which is set by the pump, was 0.384 Hz. Even so, at the pumpfrequency that suppression ratio was 648, which is close to that valuemeasured in water. This supports the idea that the PC volume iscompensating for the solvent compressibility, and that the expansion ofthe tubing plays a minor role. This also means that the system does notneed to be retuned for each solvent.

To investigate whether tubing expansion ever plays a role in the pickupof pump pulses a series of experiments were performed using PEEKcapillary tubing for the PC volume. Since PEEK has a much lower Young'smodulus than stainless steel, it expands much more than equivalentstainless steel tubing. One expects that expansion of the tubing willplay a role in addition to that from the solvent compressibility. Theprediction therefore is that a smaller volume in the PC would berequired to balance the system. FIG. 17 shows the result of measuringthe suppression ratio as a function of tubing length in aqueoussolutions. The peak in the curve corresponds to a 17 ft length of 0.030″ID PEEK tubing. The interior volume is 2.4 mL compared to 8.4 mL thatwas required when using stainless steel capillary. As expected when oneuses softer tubing, the solvent compressibility is balanced with a muchlower volume.

The four capillary bridge viscometer has been used for years as anon-line chromatography detector. However many researchers have sufferedwith limited sensitivity due to pick-up from pump pulses and otherparasitic noise sources. Until now, the fundamental promise of thebridge design to reject pump pulses has only partially been realized.With this innovative and inexpensive improvement to the bridge design,one can enhance the sensitivity to low concentration, low viscositysamples and continue to achieve high quality data even when usinginexpensive pumps.

As will be evident to those skilled in the arts of viscometricmeasurements, macromolecular characterization, and chromatography, thereare many obvious variations of the methods and devices of my inventionthat do not depart from the fundamental elements listed for theirpractice; all such variations are but obvious implementations of theinvention described hereinbefore and are included by reference to ourclaims, which follow.

What is claimed is:
 1. A capillary bridge viscometer comprising: abridge to receive a solvent delivered to the bridge by a pump systemcomprising; a first arm comprising a first pair of series connectedsensing capillaries, a second arm comprising a second pair of seriesconnected sensing capillaries, and a delay volume connected in seriesbetween the second pair of series connected sensing capillaries, whereinthe second arm is connected in parallel with the first arm, a firstdifferential pressure transducer coupled across the first arm and thesecond arm, such that the first differential pressure provides ameasurement of first amplitudes of pressure pulses generated in thesolvent by the pump system wherein the first differential pressuretransducer is coupled to the first arm at a first junction between eachof the first pair of series connected sensing capillaries, and such thatthe first differential pressure transducer is coupled to the second armat a second junction between one of the second pair of series connectedsensing capillaries and the delay volume, and a pressure compensationvolume between the first junction and to the first differential pressuretransducer to transmit pressure to the first differential pressuretransducer, wherein the pressure compensation volume comprises capillarytubing; a second differential pressure transducer providing ameasurement of second amplitudes of pressure pulses generated in thesolvent by the pump system where the second differential pressuretransducer is connected in parallel with the first arm and the secondarm; and wherein a length of the capillary tubing of the pressurecompensation volume is sized such that a fluid volume of the pressurecompensation volume matches a fluid volume of the delay volume tobalance compressibility of fluid in the delay volume by maximizing asuppression ratio where the suppression ratio is defined by peakamplitudes among the second measured pressure pulse amplitudes dividedby peak amplitudes among the first measured pressure pulse amplitudes,resulting in a minimizing of the amplitudes of pressure pulses generatedin the solvent by the pump system.
 2. The capillary bridge viscometer ofclaim 1 wherein the tubing comprises stainless steel.
 3. The capillarybridge viscometer of claim 1 further comprising a valve connected to thepressure compensation volume to permit the volume to be flushed by fluidpassing through the first arm.